Average Error: 0.0 → 0
Time: 1.2s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[\left(2 \cdot im\right) \cdot re\]
re \cdot im + im \cdot re
↓
\left(2 \cdot im\right) \cdot re
double f(double re, double im) {
        double r8046 = re;
        double r8047 = im;
        double r8048 = r8046 * r8047;
        double r8049 = r8047 * r8046;
        double r8050 = r8048 + r8049;
        return r8050;
}
↓
double f(double re, double im) {
        double r8051 = 2.0;
        double r8052 = im;
        double r8053 = r8051 * r8052;
        double r8054 = re;
        double r8055 = r8053 * r8054;
        return r8055;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re\]

  2. Simplified0

    \[\leadsto \color{blue}{\left(2 \cdot im\right) \cdot re}\]

  3. Final simplification0

    \[\leadsto \left(2 \cdot im\right) \cdot re\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))